{
  "id": "1709.00998",
  "version": "v1",
  "published": "2017-09-04T15:16:20.000Z",
  "updated": "2017-09-04T15:16:20.000Z",
  "title": "Intersections of Class Fields",
  "authors": [
    "Lars Kühne"
  ],
  "comment": "12 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Using class field theory, we prove a restriction on the intersection of the maximal abelian extensions associated with different number fields. This restriction is then used to improve a result of Rosen and Silverman about the linear independence of Heegner points. In addition, it yields effective restrictions for the special points lying on an algebraic subvariety in a product of modular curves. The latter application is related to the Andr\\'e-Oort conjecture.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-09-04T15:16:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G05",
      "11R37",
      "11G18",
      "14G35"
    ],
    "keywords": [
      "intersection",
      "maximal abelian extensions",
      "class field theory",
      "andre-oort conjecture",
      "linear independence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}